Problem: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 - 47}{x + 10} = \dfrac{53}{x + 10}$
Answer: Multiply both sides by $x + 10$ $ \dfrac{x^2 - 47}{x + 10} (x + 10) = \dfrac{53}{x + 10} (x + 10)$ $ x^2 - 47 = 53$ Subtract $53$ from both sides: $ x^2 - 47 - (53) = 53 - (53)$ $ x^2 - 47 - 53 = 0$ $ x^2 - 100 = 0$ Factor the expression: $ (x - 10)(x + 10) = 0$ Therefore $x = 10$ or $x = -10$ However, the original expression is undefined when $x = -10$. Therefore, the only solution is $x = 10$.